Integrated circuit memory devices include a semiconductor substrate and a bit line on the semiconductor substrate. A plurality of memory cells is also provided. Each of these magnetic memory cells includes a magnetic storage element, a magnetic flux focusing layer on the magnetic storage element and an electrically insulating layer extending between the bit line and the magnetic flux focusing layer. This electrically insulating layer may contact an upper surface of the magnetic flux focusing layer and a lower surface of the bit line. The magnetic memory cell further includes a non-ferromagnetic electrically conductive layer extending between the magnetic flux focusing layer and the magnetic storage element. The electrically insulating layer is configured to cause current passing in a first direction (e.g., vertical direction) from the magnetic storage element to the non-ferromagnetic electrically conductive layer during a cell writing operation to spread laterally in the magnetic flux focusing layer (and non-ferromagnetic electrically conductive layer) in a second direction (e.g., lateral direction), which is orthogonal to the first direction. The magnetic flux focusing layer may be formed of a ferromagnetic material, such as NiFe.